In order for you to play Besiege on Linux with minimal graphics settings, your computer must meet the following requirements
Operating System:
Ubuntu 12.04 or higher
Processor (CPU):
2.2Ghz Dual Core
Memory (RAM):
4 GB RAM
Graphics Card:
OpenGL 2.0 compatible, 512 MB VRAM
Storage:
3 GB available space
Sound Card:
ALSA compatible